Plot hole: Radl and Steiner discuss the entire scheme to kidnap Churchill on the Alderney docks - in full view and hearing of a number of civilians (who shouldn't be there, pace another posting), including local fishermen. Though the Germans banned all fishing activities in the Channel islands including Alderney in 1941, they were well aware that there was a flow of information from the island to military authorities in the mainland. Why would they be so stupid as to discuss a top secret military mission in public? In reality, they wouldn't even discuss it in front of their own men.
Factual error: In the aerial shot over rural Britain near the beginning of the movie, there are two modern cars visible. Too new to be early 40's models.
Factual error: When we are in the Colonel's office at the US army base there is a US flag in the corner. It has 50 stars on it, as you can tell by the pattern. There were only 48 stars on the flag during WWII.
Continuity mistake: After Kurt returns to the quay from the raid near the start, the coat of one of his men is noticeably bloodstained. Later, walking up the stairs to the pub, the bloodstain is gone. But when he pours alcohol over Devlin's arm, the bloodstain has returned.
Revealing mistake: This film has the old movie trait of Nazis having German accents rather than actually speaking in German, which is fair enough as they take up the majority of the screen time. However, not everyone adheres to this rule and there are many characters, minor and major who slip in and out of accents, and many never have them at all.
Continuity mistake: When Steiner lifts up the Jewish girl, if you look closely, you can see the rear end of the train about 20 metres away. Yet somehow Steiner has time to ask her name, wish her good luck, set her down on one of the carriages and watch her get shot before the train fully passes him. The departing train also conveniently slows down for him to drop the girl. (00:12:20)
Revealing mistake: Ms. Grey's door is kicked open by the US colonel. A split second before he kicks it, though, the door mysteriously becomes unlatched from the inside. I guess this is so the actor wouldn't hurt his leg.
Factual error: When Michael Caine is standing outside the village church, it is clearly visible that double yellow line road markings have been blacked out (covered up). The film is set during the war, but double yellow lines did not make an appearance in the UK until 1958, therefore it is clear that the filmakers blacked them out to avoid an anachronism.
Plot hole: When the general approaches Steiner in the train yard, he says 'you didn't seem so discriminating a moment ago' implying that he saw Steiner help the Jewish girl onto the train. But this is impossible, as there was a moving train between himself and Steiner when the incident happened. For all he knew Steiner could be blameless. (00:13:00)
Continuity mistake: After Donald Sutherland parachutes into England, he walks across a cow paddock towards a gate. As he climbs over the gate, you can see there are no cows to the left of him along the fence but in the very next shot, you can see a line of cows along the fence which weren't there in the previous shot. (00:39:55)
Continuity mistake: In the scene where Devlin is thrown through the pub window, his coat shows no sign of the alcohol which was poured over him.